Multispectral imaging is an important technology for acquiring and displaying precise color information, due to the following facts: firstly, a multispectral image contains more spectral information, and secondly, the multispectral imaging technology well overcomes the phenomenon of metamerism. Moreover, multispectral imaging of an ultra-weak light object particularly has a wide application prospect in multiple fields.
A typical ultra-weak light detector is a single-photon detector. The counting type single-photon detector works in a saturation state, with its sensitivity being at a single-photon level, and can acquire photon density images by adopting a statistical method; and for the single-photon detector with the resolution capacity of photon counts which works in a sub-saturation state, the amplitude of the electrical signal output by the single-photon detector varies with the number of detected photons, thereby based on this electrical signal an ultra-weak light image is acquired. Although the spectral response range of the present single-photon detectors cover the bands of infrared, visible light and the like, it is still narrow for onefold single-photon detector, which is generally used for detecting the light at a certain single frequency.
In this case, the single-photon detector realizes two-dimensional imaging based on the compressive sensing (CS for short) theory and the digital light processing technology, and solves the problem that high-quality imaging of an ultra-weak light object is difficult to realize for the reason that the existing array detection technology in ultra-weak light two-dimensional imaging technology is still immature. And it also solves the problems that the imaging time is long and the resolution is restricted by mechanical raster scan precision due to the combination of a point detector and a two-dimensional drive scanning method.
The CS theory proposed by Donoho, E. J. Candès et al., breaks through the traditional linear sampling pattern, and shows that a little portion of the linear random projection of compressive signals contains enough information for reconstructing original signals. According to the spirit of “sampling first and reconstructing subsequently”, it is possible to convert two-dimensional signals into one-dimensional signals distributed along with time and to do the sampling by a single detector.
The CS theory comprises two parts, namely compressive sampling and sparse reconstruction.
The compressive sampling is a process for mapping signals to be measured from high-dimensional signals to low-dimensional ones. If xεRn is the data to be measured, yεRk is observation data, ΦεRk×n is a random projection matrix (k<<n) and eεRk is measurement noise, then the compressive sampling process can be described as formula (1):y=Φx+e  (1)
If x is sparse in a transform domain, that is, θ=Ψx and Ψ is a sparse transform matrix, then formula (1) is transformed into formula (2):y=ΦΨθ+e  (2)
The random projection matrix Φ is also referred to as a measurement matrix, and is required to satisfy RIP (Restricted Isometry Property). In addition, the more irrelevant Φ and Ψ is, the smaller the value of the measurement times k required by sampling is, so generally Φ is designed as a random matrix.
The sparse reconstruction actually means to solve x in formula (1) under the condition that the observation data y and the measurement matrix Φ are known, which is an ill-posed problem and generally solved by using an optimization method and can be described as formula (3):
                              min                      x            ∈                          R              n                                      ⁢                  (                                                    1                2                            ⁢                                                                                      y                    -                                          Φ                      ⁢                                                                                          ⁢                      x                                                                                        2                2                                      +                          τ              ⁢                                                                  x                                                  1                                              )                                    (        3        )            
If x is sparse in some fixed basis, so the reconstruction problem of formula (3) can be described as formula (4):
                              min                      x            ∈                          R              n                                      ⁢                  (                                                    1                2                            ⁢                                                                                      y                    -                                          Φ                      ⁢                                                                                          ⁢                      x                                                                                        2                2                                      +                          τ              ⁢                                                                                      Ψ                    ⁢                                                                                  ⁢                    x                                                                    1                                              )                                    (        4        )            In formula (3) and formula (4), the first item is a least-square constraint marked as f(x); the second item is a constraint which describes the sparsity of x; and the sum of the two items is a final target function marked as φ(x).
The digital light processing technology was proposed by Texas Instruments (TI), when combined with digital video or graphical signals, its micro-mirror and lens system can reflect digital images onto a screen or other surfaces. The core of digital light processing technology is a digital light processing chip, namely digital micro-mirror device (DMD for short), which probably is the most precise optical switch in the world now. The DMD comprises a matrix of up to 2 million micro-mirrors installed on hinges, the size of each micro-mirror is smaller than one fifth of the width of human hair, and each micro-mirror can swing in a certain angle range between −12° and +12°. If the two states are marked as 0 and 1, the micro-mirrors are driven to jitter at a high speed between 0 and 1 by using pulse width modulation (PWM), so that an intermediate state can be realized. The DMD and the related precise electronic elements thereof constitute the so-called digital light processing technology.